Randomized, controlled, national, multicenter, prospective study to compare systematic rituximab infusions (conventional therapy) to rituximab infusion based on rate of ANCA and CD19 lymphocytes in patients with systemic ANCA-associated vasculitis, in remission (achieved with an induction treatment combining corticosteroids and an immunosuppressant after the first flare of the disease (new diagnosis) or after a relapse. Patients will be stratified by first flare (66% of the patients) or relapse (33% of the patients). Patients complying with the inclusion criteria may be included when they are in remission from their vasculitis. Patients will be included at the time of remission and then randomized. They will receive maintenance treatment by 1)2 rituximab infusions mg at D1, D15 then every 6 months until month 18 (i.e. a total of 5 infusions), at the dose of 500 mg. 2) 1 rituximab infusion at the dose of 500 mg at D0 then ANCA status and CD19+ lymphocyte count will be monitored every 3 months, and patients will receive new 500 mg rituximab infusions either if CD19 are > to 0/mm3, or if ANCA are positive again or if ANCA titer significantly raises. After the 18 month length of maintenance phase, i.e. after stopping immunosuppressive maintenance therapy, patients will be followed for an additional 10 month period. Patients with granulomatosis with polyangiitis will be prescribed cotrimoxazole 160/800 tid (for 2 additional years).